In our recent paper [1]}, we started to investigate knapsack and subset sum for graph groups, which are also known
as right-angled Artin groups in group theory. A graph group is specified by a finite simple graph \(\Gamma \)  and denoted with
\(\mathbb {G}(\Gamma )\) . The vertices are the generators of the group, and two generators
\(a\)  and \(b\)  are allowed to commute if and only if \(a\)  and \(b\)  are adjacent in \(\Gamma \) . Graph groups interpolate between
free groups and free abelian groups and can be seen as a group counterpart of trace monoids (free partially commutative
monoids), which have been used for the specification of concurrent behavior. In combinatorial group theory, graph groups
are currently an active area of research, mainly because of their rich subgroup structure, see e.g. [2]}, [3]}, [4]}.
